Problem: Simplify the following expression: $ a = \dfrac{-4}{9} - \dfrac{-6k - 10}{7k + 5} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7k + 5}{7k + 5}$ $ \dfrac{-4}{9} \times \dfrac{7k + 5}{7k + 5} = \dfrac{-28k - 20}{63k + 45} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-6k - 10}{7k + 5} \times \dfrac{9}{9} = \dfrac{-54k - 90}{63k + 45} $ Therefore $ a = \dfrac{-28k - 20}{63k + 45} - \dfrac{-54k - 90}{63k + 45} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-28k - 20 - (-54k - 90) }{63k + 45} $ Distribute the negative sign: $a = \dfrac{-28k - 20 + 54k + 90}{63k + 45}$ $a = \dfrac{26k + 70}{63k + 45}$